Question: $ B = \left[\begin{array}{rrr}3 & -2 & 2 \\ 0 & -2 & 4\end{array}\right]$ $ D = \left[\begin{array}{r}3 \\ 4\end{array}\right]$ Is $ B- D$ defined?
Answer: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ B$ is of dimension $( m \times  n)$ and $ D$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ B$ ) must equal $ p$ (number of rows in $ D$ ) and 2. $ n$ (number of columns in $ B$ ) must equal $ q$ (number of columns in $ D$ Do $ B$ and $ D$ have the same number of rows? Yes Yes No Yes Do $ B$ and $ D$ have the same number of columns? No Yes No No Since $ B$ has different dimensions $(2\times3)$ from $ D$ $(2\times1)$, $ B- D$ is not defined.